Baking a particle system in Blender to use in Unity
This is not possible. Particle System simulations are not supported at all due to the fact that Unity has a completely different solution. 

Unity currently imports (from blender)
all nodes with position, rotation and scale. Pivot points and Names are also imported.
Meshes with vertices, polygons, triangles, UVs, and normals.
Bones,
Skinned Meshes, and
Animations